Step 5: Simplifying Fractions

Simplifying Fractions

Often after you add, the fraction can be simplified. A fraction whose numerator and denominator both have a factor in common can be simplified. (Factors are numbers that the original number is evenly divisible by, or numbers that can be multiplied to give the original number.)

We can demonstrate this using the results of the two examples in Step 4: 6/9 and 1 2/12.

If we examine 6/9, and find the factors of the numerator and the factors of the denominator, we find:

factors of 6: 1, 2, 3, and 6 (because 1 x 6 = 6 and 2 x 3 = 6)
factors of 9: 1, 3, and 9

Since 3 is a common factor of both numbers, we can divide both the numerator and denominator by 3 and get a simplified fraction. As with multiplying both the top and bottom of the fraction by the same number, dividing them each by the same number results in an equivalent, or equal, fraction.

So 6 divided by 3 = 2,
and 9 divided by 3 = 3,

so our resulting simplified fraction = 2/3.

Likewise with 1 2/12. Looking at the fractional part of the answer and finding the factors we find:

factors of 2: 1 and 2
factors of 12: 1, 2, 3, 4, 6, and 12

Dividing both the numerator and denominator of our fraction by 2 (the greatest common factor), gives:
2 divided by 2 = 1
12 divided by 2 = 6

so our resulting simplified answer is 1 1/6.
I love ice cream!!!
meh301 gets a point!!!!!!
You make damn sense<br>
Wow, I can't believe my luck. I merely stumbled on your fantastic instructions here on the day my daughter has to study for a fractions test! So thakns so much. I really have been struggling to explain these logically to her! Now I can with ease! Well done on your deserving win too!
Glad I could help!
or 1 1/6 i thought you were simplifying all these :P
I love ice cream!
Nice Instructable and congratulations on your win! By the way, I <em><strong>love</strong></em> ice cream.<br/>
This is a good instructible. <br/><br/>I only have one small criticism:<br/><br/>It is not good practice to write mixed fractions without the addition operator. A mixed fraction is a sum, and it should be written as such, e.g.<br/><br/>3 + <sup>1</sup>/<sub>2</sub><br/><br/>The notation: <br/><br/>3 <sup>1</sup>/<sub>2</sub><br/><br/>is confusing because there is another convention that says putting two expressions side by side like that means multiplication; i.e.<br/><br/>3 <sup>1</sup>/<sub>2</sub> = 3 * <sup>1</sup>/<sub>2</sub> = <sup>3</sup>/<sub>2</sub><br/><br/>This may seem nit-picky to many of you, but this is math after all. It is good to be clear about what your expressions mean. <br/><br/>See also:<br/><a rel="nofollow" href="http://mathworld.wolfram.com/MixedFraction.html">http://mathworld.wolfram.com/MixedFraction.html</a><br/>
I was going to write an entry for this question, using pretty much exactly the "slices of pie" examples you did. Oh well- your instructable covers all the necessary ground and looks fairly clear so it looks like the question has been answered.

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